Question

When you integrate (sec²θ), what to do?

a) Apply the power rule.

b) Use the trigonometric identity (sec²θ= tanθ + C).

c) Apply the logarithmic rule.

d) Differentiate with respect to (θ).

Answer 1

To integrate sec²θ, you use the fact that it is the derivative of tanθ, so the integral is simply tanθ + C, which is the trigonometric identity for the antiderivative of sec²θ.

Step-by-step explanation:

When integrating sec²θ, the correct approach is to remember that sec²θ is the derivative of tanθ. Therefore, the integral of sec²θ with respect to θ is tanθ plus the constant of integration, C. The correct answer is b) Use the trigonometric identity (sec²θ = tanθ + C).

To integrate sec²θ, you would follow this step:

1. Recognize that the antiderivative of sec²θ is a standard result from differentiation, which tells us that d/dθ (tanθ) = sec²θ.
2. Therefore, the integral of sec²θ dθ is tanθ + C.

You do not apply the power rule, logarithmic rule, or differentiate as those do not apply to this integration problem.